AUSTIN, Texas, March 27 (Reuters) - Texas executed convicted murderer Anthony Doyle on Thursday as it kept the pace of executions steady while other states have had to postpone capital punishments because they cannot obtain drugs used in lethal injections.

Doyle, 29, was convicted of beating food delivery woman Hyun Cho, a South Korean native, to death in 2003 with a baseball bat, putting her body in a trash can and stealing her car.

Doyle was pronounced dead at 6:49 p.m. CDT (2349 GMT) at the state's death chamber in Huntsville after receiving a lethal injection. He did not make a last statement, a Department of Criminal Justice spokesman said.

Texas, which has executed more people than any other state since the U.S. Supreme Court reinstated the death penalty in 1976, has obtained a fresh batch of its execution drug pentobarbital, the Department of Criminal Justice said this month, without revealing the source.

On Thursday, a state judge ordered Texas to release the name of its new drug supplier. The state attorney general's office said it would appeal the ruling.

The decision was for two inmates due to be executed in April and had no impact on Doyle's execution.

Many other U.S. states have been struggling to obtain drugs for executions after pharmaceutical firms, mostly in Europe, imposed sales bans because they object to having medications used in lethal injections.

Oklahoma has had to postpone two executions planned for this month because it could not find drugs. Alabama said this week it has run out of one of the main drugs it uses, putting on hold executions for 16 inmates who have exhausted appeals and face capital punishment.

Several states have looked to alter the chemicals used for lethal injection and keep the suppliers' identities secret. They have also turned to lightly regulated compounding pharmacies that can mix chemicals.

But an Oklahoma judge ruled on Wednesday that the state's secrecy on its lethal injections protocols was unconstitutional, a decision that could delay executions in other states where death row inmates are planning to launch similar challenges.

Texas plans to execute five more inmates between now and the end of May, about the same number as every other state combined for the period, according to the Death Penalty Information Center, a non-profit organization which monitors capital punishment.

Doyle was the fourth person executed in Texas this year and the 512th in the state since the death penalty was reinstated.

But executions overall have been on the decline in Texas, after hitting a peak of 40 in 2000. Since 2010, Texas has averaged about 15 executions a year.

The high costs of prosecutions and the availability of a sentence of life without parole have caused capital punishment convictions to fall to about 10 or less a year in recent years.

"We are now very selective in what we choose to go after as death penalty cases, instead of deciding that every single murder that we try will be a capital case," said Susan Reed, the district attorney in San Antonio and a death penalty supporter. (Additional reporting by Jim Forsyth in San Antonio and Heide Brandes in Oklahoma City; Editing by Lisa Shumaker and Jonathan Oatis)